arXiv subjects

Ovidiu Cristinel Stoica

Publications and source records attributed to Ovidiu Cristinel Stoica.

53 records · Page 3Linked to original sources

arXiv2016

On the wavefunction collapse

Wavefunction collapse is usually seen as a discontinuous violation of the unitary evolution of a quantum system, caused by the observation. Moreover, the collapse appears to be nonlocal in a sense which seems at odds with General Relativity. In this article the possibility that the wavefunction evolves continuously and hopefully unitarily during the measurement process is analyzed. It is argued that such a solution has to be formulated using a time symmetric replacement of the initial value problem in Quantum Mechanics. Major difficulties in apparent conflict with unitary evolution are identified, but eventually its possibility is not completely ruled out. This interpretation is in a weakened sense both local and realistic, without contradicting Bell's theorem. Moreover, if it is true, it makes Quantum Mechanics consistent with General Relativity in the semiclassical framework.

quant-ph↗

arXiv2015

Quantum Measurement and Initial Conditions

Quantum measurement finds the observed system in a collapsed state, rather than in the state predicted by the Schrödinger equation. Yet there is a relatively spread opinion that the wavefunction collapse can be explained by unitary evolution (for instance in the decoherence approach, if we take into account the environment). In this article it is proven a mathematical result which severely restricts the initial conditions for which measurements have definite outcomes, if pure unitary evolution is assumed. This no-go theorem remains true even if we take the environment into account. The result does not forbid a unitary description of the measurement process, it only shows that such a description is possible only for very restricted initial conditions. The existence of such restrictions of the initial conditions can be understood in the four-dimensional block universe perspective, as a requirement of global self-consistency of the solutions of the Schrödinger equation.

quant-ph↗

arXiv2015

The Tao of It and Bit

The main mystery of quantum mechanics is contained in Wheeler's delayed choice experiment, which shows that the past is determined by our choice of what quantum property to observe. This gives the observer a participatory role in deciding the past history of the universe. Wheeler extended this participatory role to the emergence of the physical laws ("law without law"). Since what we know about the universe comes in yes/no answers to our interrogations, this led him to the idea of "it from bit" (which includes the participatory role of the observer as a key component). The yes/no answers to our observations ("bit") should always be compatible with the existence of at least a possible reality - a global solution ("it") of the Schrodinger equation. I argue that there is in fact an interplay between "it" and "bit". The requirement of global consistency leads to apparently acausal and nonlocal behavior, explaining the weirdness of quantum phenomena. As an interpretation of Wheeler's "it from bit" and "law without law", I discuss the possibility that the universe is mathematical, and that there is a "mother of all possible worlds" - named the "Axiom Zero".

quant-ph↗

arXiv2015

The geometry of singularities and the black hole information paradox

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have {\nonsing} electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.

gr-qc↗

arXiv2015

Causal Structure and Spacetime Singularities

In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is more fundamental. But there are cases when seemingly healthy causal structure and measure determine a singular metric. Here it is shown that this is not a bug, but a feature, because big-bang and black hole singularities are instances of this situation. But while the metric is special at singularities, being singular, the causal structure and the measure are not special in an explicit way at singularities. Therefore, considering the causal structure more fundamental than the metric provides a more natural framework to deal with spacetime singularities.

gr-qc↗

arXiv2014

Gauge theory at singularities

Building on author's previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the field equations at singularities are accompanied by infinities which block the evolution equations, mainly because the metric is singular, hence the usual differential operators, constructed from the metric, blow up. However, it is possible to give otherwise equivalent formulations of the Einstein, Maxwell and Yang-Mills equations, which in addition admit solutions which can be extended beyond the singularities. The main purpose of this analysis are applications to the black hole information loss paradox. An alternative approach can be made in terms of the Kaluza-Klein theory.

gr-qc↗

arXiv2014

Cartan's Structural Equations for Singular Manifolds

The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent bundle with a symmetric bilinear form which is allowed to become degenerate. But if the fundamental tensor is allowed to be degenerate, there are some obstructions in constructing the geometric objects normally associated to the fundamental tensor. Also, local orthonormal frames and coframes no longer exist, as well as the metric connection and its curvature operator. This article shows that, if the fundamental tensor is radical stationary, we can construct in a canonical way geometric objects, determined only by the fundamental form, similar to the connection and curvature forms of Cartan. In particular, if the fundamental tensor is non-degenerate, we obtain the usual connection and curvature forms of Cartan. We write analogs of Cartan's first and second structural equations. As a byproduct we will find a compact version of the Koszul formula.

math.DG↗

arXiv2014

Metric dimensional reduction at singularities with implications to Quantum Gravity

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity.

gr-qc↗

arXiv2014

On Singular Semi-Riemannian Manifolds

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no longer work, because they are based on the inverse of the metric, and on related operations like the contraction between covariant indices. In this article we develop the geometry of singular semi-Riemannian manifolds. First, we introduce an invariant and canonical contraction between covariant indices, applicable even for degenerate metrics. This contraction applies to a special type of tensor fields, which are radical-annihilator in the contracted indices. Then, we use this contraction and the Koszul form to define the covariant derivative for radical-annihilator indices of covariant tensor fields, on a class of singular semi-Riemannian manifolds named radical-stationary. We use this covariant derivative to construct the Riemann curvature, and show that on a class of singular semi-Riemannian manifolds, named semi-regular, the Riemann curvature is smooth. We apply these results to construct a version of Einstein's tensor whose density of weight 2 remains smooth even in the presence of semi-regular singularities. We can thus write a densitized version of Einstein's equation, which is smooth, and which is equivalent to the standard Einstein equation if the metric is non-degenerate.

math.DG↗

arXiv2014

Can the clicks of the detectors provide a complete description of Nature?

No matter how counterintuitive they are, quantum phenomena are all simple consequences of the laws of Quantum Mechanics. It is not needed to extend the theory with hidden mechanisms or additional principles to explain what Quantum Mechanics already predicts. This indubitable fact is often taken as supporting the view that all we can know about the universe comes from the outcomes of the quantum observations. According to this view, we can even learn the physical laws, in particular the properties of the space, particles, fields, and interactions, solely from the outcomes of the quantum observations. In this article it is shown that the unitary symmetry of the laws of Quantum Mechanics imposes severe restrictions in learning the physical laws of the universe, if we know only the observables and their outcomes.

quant-ph↗

arXiv2014

Singular General Relativity

This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported. Singularities of the form studied here allow a smooth extension of the Einstein field equations, including matter. This applies to the Big-Bang singularity of the FLRW solution. It applies to stationary black holes, in appropriate coordinates (since the standard coordinates are singular at singularity, hiding the smoothness of the metric). In these coordinates, charged black holes have the electromagnetic potential regular everywhere. Implications on Penrose's Weyl curvature hypothesis are presented. In addition, these singularities exhibit a (geo)metric dimensional reduction, which might act as a regulator for the quantum fields, including for quantum gravity, in the UV regime. This opens the perspective of perturbative renormalizability of quantum gravity without modifying General Relativity.

gr-qc↗

arXiv2014

The Geometry of Black Hole singularities

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at non-singular points, but in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity, and don't make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to making Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

gr-qc↗

arXiv2013

Global and local aspects of causality in quantum mechanics

Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of selecting part of the initial conditions of the Universe 'retroactively'. This talk aims to show that there is a global, timeless, 'bird's view' of the spacetime, which makes this mystery more reasonable. We will review some well-known quantum effects from the perspective of global consistency.

quant-ph↗

arXiv2013

Spacetimes with Singularities

We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard operations like covariant contraction, covariant derivative, and constructions like the Riemann curvature are usually prohibited by the fact that the metric is not invertible. The things become even worse at the points where the signature changes. We show that we can still do many of these operations, in a different framework which we propose. This allows the writing of an equivalent form of Einstein's equation, which works for degenerate metric too. Once we make the singularities manageable from mathematical viewpoint, we can extend analytically the black hole solutions and then choose from the maximal extensions globally hyperbolic regions. Then we find space-like foliations for these regions, with the implication that the initial data can be preserved in reasonable situations. We propose qualitative models of non-primordial and/or evaporating black holes. We supplement the material with a brief note reporting on progress made since this talk was given, which shows that we can analytically extend the Schwarzschild and Reissner-Nordstrom metrics at and beyond the singularities, and the singularities can be made degenerate and handled with the mathematical apparatus we developed.

math.DG↗

arXiv2012

An Exploration of the Singularities in General Relativity

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to write field equations, including equations which are equivalent to Einstein's at non-singular points, but remain well-defined and smooth at singularities. This class of singularities is large enough to contain isotropic singularities, warped-product singularities, including the Friedmann-Lemaitre-Robertson-Walker singularities, etc. Also a Big-Bang singularity of this type automatically satisfies Penrose's Weyl curvature hypothesis. The Schwarzschild, Reissner-Nordstrom, and Kerr-Newman singularities apparently are not of this benign type, but we can pass to coordinates in which they become benign. The charged black hole solutions Reissner-Nordstrom and Kerr-Newman can be used to model classical charged particles in General Relativity. Their electromagnetic potential and electromagnetic field are analytic in the new coordinates - they have finite values at r=0. There are hints from Quantum Field Theory and Quantum Gravity that a dimensional reduction is required at small scale. A possible explanation is provided by benign singularities, because some of their properties correspond to a reduction of dimensionality.

gr-qc↗

arXiv2012

Analytic Reissner-Nordstrom Singularity

An analytic extension of the Reissner-Nordstrom solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at $r=0$. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension it is shown that the charged and non-rotating black hole singularities are compatible with the global hyperbolicity and with the conservation of the initial value data. Geometric models for electrically charged particles are obtained.

gr-qc↗

arXiv2011

Tensor Operations on Degenerate Inner Product Spaces

Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index lowering operation is not invertible, and (2) we cannot associate to the inner product in a canonical way a reciprocal inner product on the dual of the vector space. This article shows how these obstructions can be avoided naturally, allowing a canonical definition of covariant contraction for some important special cases. The primary motivation of this article is to lay down the algebraic foundation for the construction of invariants in Singular Semi-Riemannian Geometry, especially those related to the curvature. It turns out that the operations discussed here are enough for this purpose (arXiv:1105.0201, arXiv:1105.3404, arXiv:1111.0646). Such invariants can be applied to the study of singularities in the theory of General Relativity (arXiv:1111.4837, arXiv:1111.4332, arXiv:1111.7082, arXiv:1108.5099, arXiv:1112.4508).

math-ph↗